YES
Time: 0.013

Problem:
 Equations:
  
 TRS:
  pAC(x,zero()) -> x
  pAC(x,i(x)) -> zero()
  pAC(i(x),x) -> zero()
  pAC(a(),a()) -> zero()
  pAC(b(),b()) -> zero()
  pAC(pAC(pAC(pAC(pAC(a(),b()),a()),b()),a()),b()) -> zero()

Proof:
 AC-RPO Processor:
  precedence:
   pAC > zero > b > a > i
  status:
   
  problem:
   Equations:
    
   TRS:
    
  Qed